The star drew comparisons between Meghan and the media's obsession with her late mother-in-law Princess Diana, who died in a auto accident after being chased by photographers. "And we've seen how that ends", Clooney added, according to PA.
The "Money Monster" star laughed off suggestions he could be a godfather to Meghan and Harry's baby.
"Women, in particular, are constantly pitted against and compared with each other in a way that reminds me of how people tried to portray Diana and me all the time as rivals, which is something neither of us ever really felt", she said.
He has repeatedly complained that his relationship with his daughter has broken down and made numerous public appeals for her to get in touch with him, including an appearance on Good Morning Britain.
The letter's existence was revealed when five of Meghan's pals anonymously spoke out to defend pregnant Meghan, 37, saying she had tried reaching out to her dad but instead been met with a request to do a photo shoot together.
Meghan addressed the letter to "Daddy", before telling him she "does not understand" why he has "chosen to take this path".More news: Gervonta Davis to fight Tenshin Nasukawa in Exhibition
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Thomas Markle Snr says the letter was sent by his daughter.
"They're just chasing Meghan Markle everywhere, she's been pursued and vilified", Clooney told Australian magazine WHO.
Meghan also admonishes her father for siding with her half-sister Samantha - who has attacked her in the press - while she "silently suffered at the hand of her vicious lies".
Last week one paper published a highly personal letter they said was written by Markle to her estranged father in which she begged him to "stop lying.stop exploiting my relationship with my husband".
Meghan Markle and Prince Harry stepped out for a gala night for a new play that heralds a cause close to their hearts on Tuesday.
"She told them both that the whole thing was becoming a nightmare, and that they should try and sort things out", a source said.
In the handwritten note, Meghan said: "We all rallied around to support and protect you from day 1, and this you know".